Related papers: Two-particle calculations with quantics tensor tra…
In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches:…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral…
Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…
We introduce a fully discrete scheme to solve a class of high-dimensional Mean Field Games systems. Our approach couples semi-Lagrangian (SL) time discretizations with Tensor-Train (TT) decompositions to tame the curse of dimensionality. By…
We introduce CL-QAS, a continual quantum architecture search framework that mitigates the challenges of costly amplitude encoding and catastrophic forgetting in variational quantum circuits. The method uses Tensor-Train encoding to…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today,…
Point-mass filters solve Bayesian recursive relations by approximating probability density functions of a system state over grids of discrete points. The approach suffers from the curse of dimensionality. The exponential increase of the…
We present an implementation of a truncated unity parquet solver (TUPS) which solves the parquet equations using a truncated form-factor basis for the fermionic momenta. This way fluctuations from different scattering channels are treated…
Circuit knitting offers a promising path to the scalable execution of large quantum circuits by breaking them into smaller sub-circuits whose output is recombined through classical postprocessing. However, current techniques face excessive…
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…
In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…
If $\Psi$ is a quaternionic wave function, then $i\Psi\neq \Psi i$. Thus, there are two versions of the quaternionic Schr\"odinger equation (QSE). In this article, we present the second possibility for solving the QSE, following on from a…
Recently, it has been presented some algorithms and physical models which give prospects for construction of quantum computers capable to solve systems of linear equations. The common feature which is shared in these works is the use of…
Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…
Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that…
Space-time dependence of imaginary-time propagators, vital for \textit{ab initio} and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X {\bf 13},…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…